Multiple Magnetorotons and Spectral Sum Rules in Fractional Quantum Hall Systems

Dung Xuan Nguyen; F D M Haldane; E H Rezayi; Dam Thanh Son; Kun Yang

doi:10.1103/PhysRevLett.128.246402

Multiple Magnetorotons and Spectral Sum Rules in Fractional Quantum Hall Systems

Phys Rev Lett. 2022 Jun 17;128(24):246402. doi: 10.1103/PhysRevLett.128.246402.

Authors

Dung Xuan Nguyen¹, F D M Haldane², E H Rezayi³, Dam Thanh Son⁴, Kun Yang⁵

Affiliations

¹ Brown Theoretical Physics Center and Department of Physics, Brown University, 182 Hope Street, Providence, Rhode Island 02912, USA.
² Department of Physics, Princeton University, Princeton, New Jersey 08544, USA.
³ Physics Department, California State University Los Angeles, Los Angeles, California 90032, USA.
⁴ Kadanoff Center for Theoretical Physics, University of Chicago, Chicago, Illinois 60637, USA.
⁵ NHMFL and Department of Physics, Florida State University, Tallahassee, Florida 32306, USA.

PMID: 35776452
DOI: 10.1103/PhysRevLett.128.246402

Abstract

We study, numerically, the charge neutral excitations (magnetorotons) in fractional quantum Hall systems, concentrating on the two Jain states near quarter filling, ν=2/7 and ν=2/9, and the ν=1/4 Fermi-liquid state itself. In contrast to the ν=1/3 states and the Jain states near half filling, on each of the two Jain states ν=2/7 and ν=2/9 the graviton spectral densities show two, instead of one, magnetoroton peaks. The magnetorotons have spin 2 and have opposite chiralities in the ν=2/7 state and the same chirality in the ν=2/9 state. We also provide a numerical verification of a sum rule relating the guiding center spin s[over ¯] with the spectral densities of the stress tensor.